augmentedRCBD OutputR/gva.augmentedRCBD.R
gva.augmentedRCBD.Rdgva.augmentedRCBD performs genetic variability analysis on an object of
class augmentedRCBD.
gva.augmentedRCBD(aug, k = 2.063)A list with the following descriptive statistics:
The mean value.
Phenotyic variance.
Genotyipc variance.
Environmental variance.
Genotypic coefficient of variation
The \(GCV\) category according to Sivasubramaniam and Madhavamenon (1973) .
Phenotypic coefficient of variation
The \(PCV\) category according to Sivasubramaniam and Madhavamenon (1973) .
Environmental coefficient of variation
The broad-sense heritability (\(H^{2}\)) (Lush 1940) .
The \(H^{2}\) category according to Robinson (1966) .
Genetic advance (Johnson et al. 1955) .
Genetic advance as per cent of mean (Johnson et al. 1955) .
The \(GAM\) category according to Johnson et al. (1955) .
gva.augmentedRCBD performs genetic variability analysis from the ANOVA
results in an object of class augmentedRCBD and computes several
variability estimates.
The phenotypic, genotypic and environmental variance (\(\sigma^{2}_{p}\), \(\sigma^{2}_{g}\) and \(\sigma^{2}_{e}\) ) are obtained from the ANOVA tables according to the expected value of mean square described by Federer and Searle (1976) as follows:
\[\sigma^{2}_{g} = \sigma^{2}_{p} - \sigma^{2}_{e}\]
Phenotypic and genotypic coefficients of variation (\(PCV\) and \(GCV\)) are estimated according to Burton (1951, 1952) as follows:
\[GCV = \frac{\sigma^{2}_{g}}{\sqrt{\overline{x}}} \times 100\]
Where \(\overline{x}\) is the mean.
The estimates of \(PCV\) and \(GCV\) are categorised according to Sivasubramanian and Madhavamenon (1978) as follows:
| CV (%) | Category |
| x \( | Low |
| 10 \(\le\) x \( | Medium |
| \(\ge\) 20 | High |
The broad-sense heritability (\(H^{2}\)) is calculated according to method of Lush (1940) as follows:
\[H^{2} = \frac{\sigma^{2}_{g}}{\sigma^{2}_{p}}\]
The estimates of broad-sense heritability (\(H^{2}\)) are categorised according to Robinson (1966) as follows:
| \(H^{2}\) | Category |
| x \( | Low |
| 30 \(\le\) x \( | Medium |
| \(\ge\) 60 | High |
Genetic advance (\(GA\)) is estimated and categorised according to Johnson et al., (1955) as follows:
\[GA = k \times \sigma_{g} \times \frac{H^{2}}{100}\]
Where the constant \(k\) is the standardized selection differential or selection intensity. The value of \(k\) at 5% proportion selected is 2.063. Values of \(k\) at other selected proportions are available in Appendix Table A of Falconer and Mackay (1996).
Selection intensity (\(k\)) can also be computed in R as below:
If p is the proportion of selected individuals, then deviation of
truncation point from mean (x) and selection intensity (k) are
as follows:
x = qnorm(1-p)
k = dnorm(qnorm(1 - p))/p
Using the same the Appendix Table A of Falconer and Mackay (1996) can be recreated as follows.
TableA <- data.frame(p = c(seq(0.01, 0.10, 0.01), NA,
seq(0.10, 0.50, 0.02), NA,
seq(1, 5, 0.2), NA,
seq(5, 10, 0.5), NA,
seq(10, 50, 1)))
TableA$x <- qnorm(1-(TableA$p/100))
TableA$i <- dnorm(qnorm(1 - (TableA$p/100)))/(TableA$p/100)Appendix Table A (Falconer and Mackay, 1996)
| p% | x | i |
| 0.01 | 3.71901649 | 3.9584797 |
| 0.02 | 3.54008380 | 3.7892117 |
| 0.03 | 3.43161440 | 3.6869547 |
| 0.04 | 3.35279478 | 3.6128288 |
| 0.05 | 3.29052673 | 3.5543807 |
| 0.06 | 3.23888012 | 3.5059803 |
| 0.07 | 3.19465105 | 3.4645890 |
| 0.08 | 3.15590676 | 3.4283756 |
| 0.09 | 3.12138915 | 3.3961490 |
| 0.10 | 3.09023231 | 3.3670901 |
| <> | <> | <> |
| 0.10 | 3.09023231 | 3.3670901 |
| 0.12 | 3.03567237 | 3.3162739 |
| 0.14 | 2.98888227 | 3.2727673 |
| 0.16 | 2.94784255 | 3.2346647 |
| 0.18 | 2.91123773 | 3.2007256 |
| 0.20 | 2.87816174 | 3.1700966 |
| 0.22 | 2.84796329 | 3.1421647 |
| 0.24 | 2.82015806 | 3.1164741 |
| 0.26 | 2.79437587 | 3.0926770 |
| 0.28 | 2.77032723 | 3.0705013 |
| 0.30 | 2.74778139 | 3.0497304 |
| 0.32 | 2.72655132 | 3.0301887 |
| 0.34 | 2.70648331 | 3.0117321 |
| 0.36 | 2.68744945 | 2.9942406 |
| 0.38 | 2.66934209 | 2.9776133 |
| 0.40 | 2.65206981 | 2.9617646 |
| 0.42 | 2.63555424 | 2.9466212 |
| 0.44 | 2.61972771 | 2.9321196 |
| 0.46 | 2.60453136 | 2.9182048 |
| 0.48 | 2.58991368 | 2.9048286 |
| 0.50 | 2.57582930 | 2.8919486 |
| <> | <> | <> |
| 1.00 | 2.32634787 | 2.6652142 |
| 1.20 | 2.25712924 | 2.6028159 |
| 1.40 | 2.19728638 | 2.5490627 |
| 1.60 | 2.14441062 | 2.5017227 |
| 1.80 | 2.09692743 | 2.4593391 |
| 2.00 | 2.05374891 | 2.4209068 |
| 2.20 | 2.01409081 | 2.3857019 |
| 2.40 | 1.97736843 | 2.3531856 |
| 2.60 | 1.94313375 | 2.3229451 |
| 2.80 | 1.91103565 | 2.2946575 |
| 3.00 | 1.88079361 | 2.2680650 |
| 3.20 | 1.85217986 | 2.2429584 |
| 3.40 | 1.82500682 | 2.2191656 |
| 3.60 | 1.79911811 | 2.1965431 |
| 3.80 | 1.77438191 | 2.1749703 |
| 4.00 | 1.75068607 | 2.1543444 |
| 4.20 | 1.72793432 | 2.1345772 |
| 4.40 | 1.70604340 | 2.1155928 |
| 4.60 | 1.68494077 | 2.0973249 |
| 4.80 | 1.66456286 | 2.0797152 |
| 5.00 | 1.64485363 | 2.0627128 |
| <> | <> | <> |
| 5.00 | 1.64485363 | 2.0627128 |
| 5.50 | 1.59819314 | 2.0225779 |
| 6.00 | 1.55477359 | 1.9853828 |
| 6.50 | 1.51410189 | 1.9506784 |
| 7.00 | 1.47579103 | 1.9181131 |
| 7.50 | 1.43953147 | 1.8874056 |
| 8.00 | 1.40507156 | 1.8583278 |
| 8.50 | 1.37220381 | 1.8306916 |
| 9.00 | 1.34075503 | 1.8043403 |
| 9.50 | 1.31057911 | 1.7791417 |
| 10.00 | 1.28155157 | 1.7549833 |
| <> | <> | <> |
| 10.00 | 1.28155157 | 1.7549833 |
| 11.00 | 1.22652812 | 1.7094142 |
| 12.00 | 1.17498679 | 1.6670040 |
| 13.00 | 1.12639113 | 1.6272701 |
| 14.00 | 1.08031934 | 1.5898336 |
| 15.00 | 1.03643339 | 1.5543918 |
| 16.00 | 0.99445788 | 1.5206984 |
| 17.00 | 0.95416525 | 1.4885502 |
| 18.00 | 0.91536509 | 1.4577779 |
| 19.00 | 0.87789630 | 1.4282383 |
| 20.00 | 0.84162123 | 1.3998096 |
| 21.00 | 0.80642125 | 1.3723871 |
| 22.00 | 0.77219321 | 1.3458799 |
| 23.00 | 0.73884685 | 1.3202091 |
| 24.00 | 0.70630256 | 1.2953050 |
| 25.00 | 0.67448975 | 1.2711063 |
| 26.00 | 0.64334541 | 1.2475585 |
| 27.00 | 0.61281299 | 1.2246130 |
| 28.00 | 0.58284151 | 1.2022262 |
| 29.00 | 0.55338472 | 1.1803588 |
| 30.00 | 0.52440051 | 1.1589754 |
| 31.00 | 0.49585035 | 1.1380436 |
| 32.00 | 0.46769880 | 1.1175342 |
| 33.00 | 0.43991317 | 1.0974204 |
| 34.00 | 0.41246313 | 1.0776774 |
| 35.00 | 0.38532047 | 1.0582829 |
| 36.00 | 0.35845879 | 1.0392158 |
| 37.00 | 0.33185335 | 1.0204568 |
| 38.00 | 0.30548079 | 1.0019882 |
| 39.00 | 0.27931903 | 0.9837932 |
| 40.00 | 0.25334710 | 0.9658563 |
| 41.00 | 0.22754498 | 0.9481631 |
| 42.00 | 0.20189348 | 0.9306998 |
| 43.00 | 0.17637416 | 0.9134539 |
| 44.00 | 0.15096922 | 0.8964132 |
| 45.00 | 0.12566135 | 0.8795664 |
| 46.00 | 0.10043372 | 0.8629028 |
| 47.00 | 0.07526986 | 0.8464123 |
| 48.00 | 0.05015358 | 0.8300851 |
| 49.00 | 0.02506891 | 0.8139121 |
| 50.00 | 0.00000000 | 0.7978846 |
Where p% is the selected percentage of individuals from a population, x is the deviation of the point of truncation of selected individuals from population mean and i is the selection intensity.
Genetic advance as per cent of mean (\(GAM\)) are estimated and categorised according to Johnson et al., (1955) as follows:
\[GAM = \frac{GA}{\overline{x}} \times 100\]
| GAM | Category |
| x \( | Low |
| 10 \(\le\) x \( | Medium |
| \(\ge\) 20 | High |
Genetic variability analysis needs to be performed only if the sum of squares of "Treatment: Test" are significant.
Negative estimates of variance components if computed are not abnormal. For information on how to deal with these, refer Robinson (1955) and Dudley and Moll (1969).
Lush JL (1940). “Intra-sire correlations or regressions of offspring on dam as a method of estimating heritability of characteristics.” Proceedings of the American Society of Animal Nutrition, 1940(1), 293–301.
Burton GW (1951). “Quantitative inheritance in pearl millet (Pennisetum glaucum).” Agronomy Journal, 43(9), 409–417.
Burton GW (1952). “Qualitative inheritance in grasses. Vol. 1.” In Proceedings of the 6th International Grassland Congress, Pennsylvania State College, 17–23.
Johnson HW, Robinson HF, Comstock RE (1955). “Estimates of genetic and environmental variability in soybeans.” Agronomy journal, 47(7), 314–318.
Robinson HF, Comstock RE, Harvey PH (1955). “Genetic variances in open pollinated varieties of corn.” Genetics, 40(1), 45–60.
Robinson HF (1966). “Quantitative genetics in relation to breeding on centennial of Mendelism.” Indian Journal of Genetics and Plant Breeding, 171.
Dudley JW, Moll RH (1969). “Interpretation and use of estimates of heritability and genetic variances in plant breeding.” Crop Science, 9(3), 257–262.
Sivasubramaniam S, Madhavamenon P (1973). “Genotypic and phenotypic variability in rice.” The Madras Agricultural Journal, 60(9-13), 1093–1096.
Federer WT, Searle SR (1976). “Model Considerations and Variance Component Estimation in Augmented Completely Randomized and Randomized Complete Blocks Designs-Preliminary Version.” Technical Report BU-592-M, Cornell University, New York.
Falconer DS, Mackay TFC (1996). Introduction to Quantitative Genetics. Pearson/Prenctice Hall, New York, NY.
# Example data
blk <- c(rep(1,7),rep(2,6),rep(3,7))
trt <- c(1, 2, 3, 4, 7, 11, 12, 1, 2, 3, 4, 5, 9, 1, 2, 3, 4, 8, 6, 10)
y1 <- c(92, 79, 87, 81, 96, 89, 82, 79, 81, 81, 91, 79, 78, 83, 77, 78, 78,
70, 75, 74)
y2 <- c(258, 224, 238, 278, 347, 300, 289, 260, 220, 237, 227, 281, 311, 250,
240, 268, 287, 226, 395, 450)
data <- data.frame(blk, trt, y1, y2)
# Convert block and treatment to factors
data$blk <- as.factor(data$blk)
data$trt <- as.factor(data$trt)
# Results for variable y1
out1 <- augmentedRCBD(data$blk, data$trt, data$y1, method.comp = "lsd",
alpha = 0.05, group = TRUE, console = TRUE)
#>
#> Augmented Design Details
#> ========================
#>
#> Number of blocks "3"
#> Number of treatments "12"
#> Number of check treatments "4"
#> Number of test treatments "8"
#> Check treatments "1, 2, 3, 4"
#>
#>
#> ANOVA, Treatment Adjusted
#> =========================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Block (ignoring Treatments) 2 360.1 180.04 6.675 0.0298 *
#> Treatment (eliminating Blocks) 11 285.1 25.92 0.961 0.5499
#> Treatment: Check 3 52.9 17.64 0.654 0.6092
#> Treatment: Test and Test vs. Check 8 232.2 29.02 1.076 0.4779
#> Residuals 6 161.8 26.97
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> ANOVA, Block Adjusted
#> =====================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Treatment (ignoring Blocks) 11 575.7 52.33 1.940 0.215
#> Treatment: Check 3 52.9 17.64 0.654 0.609
#> Treatment: Test 7 505.9 72.27 2.679 0.125
#> Treatment: Test vs. Check 1 16.9 16.87 0.626 0.459
#> Block (eliminating Treatments) 2 69.5 34.75 1.288 0.342
#> Residuals 6 161.8 26.97
#>
#> Coefficient of Variation
#> ========================
#> 6.372367
#>
#> Overall Adjusted Mean
#> =====================
#> 81.0625
#>
#> Standard Errors
#> ===============
#> Std. Error of Diff. CD (5%)
#> Control Treatment Means 4.240458 10.37603
#> Two Test Treatments (Same Block) 7.344688 17.97180
#> Two Test Treatments (Different Blocks) 8.211611 20.09309
#> A Test Treatment and a Control Treatment 6.704752 16.40594
#>
#> Treatment Means
#> ===============
#> Treatment Block Means SE r Min Max Adjusted Means
#> 1 84.67 3.84 3 79.00 92.00 84.67
#> 10 3 74.00 <NA> 1 74.00 74.00 77.25
#> 11 1 89.00 <NA> 1 89.00 89.00 86.50
#> 12 1 82.00 <NA> 1 82.00 82.00 79.50
#> 2 79.00 1.15 3 77.00 81.00 79.00
#> 3 82.00 2.65 3 78.00 87.00 82.00
#> 4 83.33 3.93 3 78.00 91.00 83.33
#> 5 2 79.00 <NA> 1 79.00 79.00 78.25
#> 6 3 75.00 <NA> 1 75.00 75.00 78.25
#> 7 1 96.00 <NA> 1 96.00 96.00 93.50
#> 8 3 70.00 <NA> 1 70.00 70.00 73.25
#> 9 2 78.00 <NA> 1 78.00 78.00 77.25
#>
#>
#> Comparisons
#> ===========
#>
#> Method : lsd
#>
#> contrast estimate SE df t.ratio p.value sig
#> treatment1 - treatment2 5.67 4.24 6 1.336 0.230
#> treatment1 - treatment3 2.67 4.24 6 0.629 0.553
#> treatment1 - treatment4 1.33 4.24 6 0.314 0.764
#> treatment1 - treatment5 6.42 6.36 6 1.009 0.352
#> treatment1 - treatment6 6.42 6.36 6 1.009 0.352
#> treatment1 - treatment7 -8.83 6.36 6 -1.389 0.214
#> treatment1 - treatment8 11.42 6.36 6 1.795 0.123
#> treatment1 - treatment9 7.42 6.36 6 1.166 0.288
#> treatment1 - treatment10 7.42 6.36 6 1.166 0.288
#> treatment1 - treatment11 -1.83 6.36 6 -0.288 0.783
#> treatment1 - treatment12 5.17 6.36 6 0.812 0.448
#> treatment2 - treatment3 -3.00 4.24 6 -0.707 0.506
#> treatment2 - treatment4 -4.33 4.24 6 -1.022 0.346
#> treatment2 - treatment5 0.75 6.36 6 0.118 0.910
#> treatment2 - treatment6 0.75 6.36 6 0.118 0.910
#> treatment2 - treatment7 -14.50 6.36 6 -2.280 0.063
#> treatment2 - treatment8 5.75 6.36 6 0.904 0.401
#> treatment2 - treatment9 1.75 6.36 6 0.275 0.792
#> treatment2 - treatment10 1.75 6.36 6 0.275 0.792
#> treatment2 - treatment11 -7.50 6.36 6 -1.179 0.283
#> treatment2 - treatment12 -0.50 6.36 6 -0.079 0.940
#> treatment3 - treatment4 -1.33 4.24 6 -0.314 0.764
#> treatment3 - treatment5 3.75 6.36 6 0.590 0.577
#> treatment3 - treatment6 3.75 6.36 6 0.590 0.577
#> treatment3 - treatment7 -11.50 6.36 6 -1.808 0.121
#> treatment3 - treatment8 8.75 6.36 6 1.376 0.218
#> treatment3 - treatment9 4.75 6.36 6 0.747 0.483
#> treatment3 - treatment10 4.75 6.36 6 0.747 0.483
#> treatment3 - treatment11 -4.50 6.36 6 -0.707 0.506
#> treatment3 - treatment12 2.50 6.36 6 0.393 0.708
#> treatment4 - treatment5 5.08 6.36 6 0.799 0.455
#> treatment4 - treatment6 5.08 6.36 6 0.799 0.455
#> treatment4 - treatment7 -10.17 6.36 6 -1.598 0.161
#> treatment4 - treatment8 10.08 6.36 6 1.585 0.164
#> treatment4 - treatment9 6.08 6.36 6 0.956 0.376
#> treatment4 - treatment10 6.08 6.36 6 0.956 0.376
#> treatment4 - treatment11 -3.17 6.36 6 -0.498 0.636
#> treatment4 - treatment12 3.83 6.36 6 0.603 0.569
#> treatment5 - treatment6 0.00 8.21 6 0.000 1.000
#> treatment5 - treatment7 -15.25 8.21 6 -1.857 0.113
#> treatment5 - treatment8 5.00 8.21 6 0.609 0.565
#> treatment5 - treatment9 1.00 7.34 6 0.136 0.896
#> treatment5 - treatment10 1.00 8.21 6 0.122 0.907
#> treatment5 - treatment11 -8.25 8.21 6 -1.005 0.354
#> treatment5 - treatment12 -1.25 8.21 6 -0.152 0.884
#> treatment6 - treatment7 -15.25 8.21 6 -1.857 0.113
#> treatment6 - treatment8 5.00 7.34 6 0.681 0.521
#> treatment6 - treatment9 1.00 8.21 6 0.122 0.907
#> treatment6 - treatment10 1.00 7.34 6 0.136 0.896
#> treatment6 - treatment11 -8.25 8.21 6 -1.005 0.354
#> treatment6 - treatment12 -1.25 8.21 6 -0.152 0.884
#> treatment7 - treatment8 20.25 8.21 6 2.466 0.049 *
#> treatment7 - treatment9 16.25 8.21 6 1.979 0.095
#> treatment7 - treatment10 16.25 8.21 6 1.979 0.095
#> treatment7 - treatment11 7.00 7.34 6 0.953 0.377
#> treatment7 - treatment12 14.00 7.34 6 1.906 0.105
#> treatment8 - treatment9 -4.00 8.21 6 -0.487 0.643
#> treatment8 - treatment10 -4.00 7.34 6 -0.545 0.606
#> treatment8 - treatment11 -13.25 8.21 6 -1.614 0.158
#> treatment8 - treatment12 -6.25 8.21 6 -0.761 0.475
#> treatment9 - treatment10 -0.00 8.21 6 -0.000 1.000
#> treatment9 - treatment11 -9.25 8.21 6 -1.126 0.303
#> treatment9 - treatment12 -2.25 8.21 6 -0.274 0.793
#> treatment10 - treatment11 -9.25 8.21 6 -1.126 0.303
#> treatment10 - treatment12 -2.25 8.21 6 -0.274 0.793
#> treatment11 - treatment12 7.00 7.34 6 0.953 0.377
#>
#> Treatment Groups
#> ================
#>
#> Method : lsd
#>
#> Treatment Adjusted Means SE df lower.CL upper.CL Group
#> 8 73.25 5.61 6 59.52 86.98 1
#> 9 77.25 5.61 6 63.52 90.98 12
#> 10 77.25 5.61 6 63.52 90.98 12
#> 5 78.25 5.61 6 64.52 91.98 12
#> 6 78.25 5.61 6 64.52 91.98 12
#> 2 79.00 3.00 6 71.66 86.34 12
#> 12 79.50 5.61 6 65.77 93.23 12
#> 3 82.00 3.00 6 74.66 89.34 12
#> 4 83.33 3.00 6 76.00 90.67 12
#> 1 84.67 3.00 6 77.33 92.00 12
#> 11 86.50 5.61 6 72.77 100.23 12
#> 7 93.50 5.61 6 79.77 107.23 2
# Results for variable y2
out2 <- augmentedRCBD(data$blk, data$trt, data$y2, method.comp = "lsd",
alpha = 0.05, group = TRUE, console = TRUE)
#>
#> Augmented Design Details
#> ========================
#>
#> Number of blocks "3"
#> Number of treatments "12"
#> Number of check treatments "4"
#> Number of test treatments "8"
#> Check treatments "1, 2, 3, 4"
#>
#>
#> ANOVA, Treatment Adjusted
#> =========================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Block (ignoring Treatments) 2 7019 3510 12.261 0.007597 **
#> Treatment (eliminating Blocks) 11 58965 5360 18.727 0.000920 ***
#> Treatment: Check 3 2150 717 2.504 0.156116
#> Treatment: Test and Test vs. Check 8 56815 7102 24.810 0.000473 ***
#> Residuals 6 1718 286
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> ANOVA, Block Adjusted
#> =====================
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Treatment (ignoring Blocks) 11 64708 5883 20.550 0.000707 ***
#> Treatment: Check 3 2150 717 2.504 0.156116
#> Treatment: Test 7 34863 4980 17.399 0.001366 **
#> Treatment: Test vs. Check 1 27694 27694 96.749 6.36e-05 ***
#> Block (eliminating Treatments) 2 1277 639 2.231 0.188645
#> Residuals 6 1717 286
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Coefficient of Variation
#> ========================
#> 6.057617
#>
#> Overall Adjusted Mean
#> =====================
#> 298.4792
#>
#> Standard Errors
#> ===============
#> Std. Error of Diff. CD (5%)
#> Control Treatment Means 13.81424 33.80224
#> Two Test Treatments (Same Block) 23.92697 58.54719
#> Two Test Treatments (Different Blocks) 26.75117 65.45775
#> A Test Treatment and a Control Treatment 21.84224 53.44603
#>
#> Treatment Means
#> ===============
#> Treatment Block Means SE r Min Max Adjusted Means
#> 1 256.00 3.06 3 250.00 260.00 256.00
#> 10 3 450.00 <NA> 1 450.00 450.00 437.67
#> 11 1 300.00 <NA> 1 300.00 300.00 299.42
#> 12 1 289.00 <NA> 1 289.00 289.00 288.42
#> 2 228.00 6.11 3 220.00 240.00 228.00
#> 3 247.67 10.17 3 237.00 268.00 247.67
#> 4 264.00 18.68 3 227.00 287.00 264.00
#> 5 2 281.00 <NA> 1 281.00 281.00 293.92
#> 6 3 395.00 <NA> 1 395.00 395.00 382.67
#> 7 1 347.00 <NA> 1 347.00 347.00 346.42
#> 8 3 226.00 <NA> 1 226.00 226.00 213.67
#> 9 2 311.00 <NA> 1 311.00 311.00 323.92
#>
#>
#> Comparisons
#> ===========
#>
#> Method : lsd
#>
#> contrast estimate SE df t.ratio p.value sig
#> treatment1 - treatment2 28.00 13.81 6 2.027 0.089
#> treatment1 - treatment3 8.33 13.81 6 0.603 0.568
#> treatment1 - treatment4 -8.00 13.81 6 -0.579 0.584
#> treatment1 - treatment5 -37.92 20.72 6 -1.830 0.117
#> treatment1 - treatment6 -126.67 20.72 6 -6.113 0.001 ***
#> treatment1 - treatment7 -90.42 20.72 6 -4.363 0.005 **
#> treatment1 - treatment8 42.33 20.72 6 2.043 0.087
#> treatment1 - treatment9 -67.92 20.72 6 -3.278 0.017 *
#> treatment1 - treatment10 -181.67 20.72 6 -8.767 0.000 ***
#> treatment1 - treatment11 -43.42 20.72 6 -2.095 0.081
#> treatment1 - treatment12 -32.42 20.72 6 -1.564 0.169
#> treatment2 - treatment3 -19.67 13.81 6 -1.424 0.204
#> treatment2 - treatment4 -36.00 13.81 6 -2.606 0.040 *
#> treatment2 - treatment5 -65.92 20.72 6 -3.181 0.019 *
#> treatment2 - treatment6 -154.67 20.72 6 -7.464 0.000 ***
#> treatment2 - treatment7 -118.42 20.72 6 -5.715 0.001 **
#> treatment2 - treatment8 14.33 20.72 6 0.692 0.515
#> treatment2 - treatment9 -95.92 20.72 6 -4.629 0.004 **
#> treatment2 - treatment10 -209.67 20.72 6 -10.118 0.000 ***
#> treatment2 - treatment11 -71.42 20.72 6 -3.447 0.014 *
#> treatment2 - treatment12 -60.42 20.72 6 -2.916 0.027 *
#> treatment3 - treatment4 -16.33 13.81 6 -1.182 0.282
#> treatment3 - treatment5 -46.25 20.72 6 -2.232 0.067
#> treatment3 - treatment6 -135.00 20.72 6 -6.515 0.001 ***
#> treatment3 - treatment7 -98.75 20.72 6 -4.766 0.003 **
#> treatment3 - treatment8 34.00 20.72 6 1.641 0.152
#> treatment3 - treatment9 -76.25 20.72 6 -3.680 0.010 *
#> treatment3 - treatment10 -190.00 20.72 6 -9.169 0.000 ***
#> treatment3 - treatment11 -51.75 20.72 6 -2.497 0.047 *
#> treatment3 - treatment12 -40.75 20.72 6 -1.967 0.097
#> treatment4 - treatment5 -29.92 20.72 6 -1.444 0.199
#> treatment4 - treatment6 -118.67 20.72 6 -5.727 0.001 **
#> treatment4 - treatment7 -82.42 20.72 6 -3.977 0.007 **
#> treatment4 - treatment8 50.33 20.72 6 2.429 0.051
#> treatment4 - treatment9 -59.92 20.72 6 -2.892 0.028 *
#> treatment4 - treatment10 -173.67 20.72 6 -8.381 0.000 ***
#> treatment4 - treatment11 -35.42 20.72 6 -1.709 0.138
#> treatment4 - treatment12 -24.42 20.72 6 -1.178 0.283
#> treatment5 - treatment6 -88.75 26.75 6 -3.318 0.016 *
#> treatment5 - treatment7 -52.50 26.75 6 -1.963 0.097
#> treatment5 - treatment8 80.25 26.75 6 3.000 0.024 *
#> treatment5 - treatment9 -30.00 23.93 6 -1.254 0.257
#> treatment5 - treatment10 -143.75 26.75 6 -5.374 0.002 **
#> treatment5 - treatment11 -5.50 26.75 6 -0.206 0.844
#> treatment5 - treatment12 5.50 26.75 6 0.206 0.844
#> treatment6 - treatment7 36.25 26.75 6 1.355 0.224
#> treatment6 - treatment8 169.00 23.93 6 7.063 0.000 ***
#> treatment6 - treatment9 58.75 26.75 6 2.196 0.070
#> treatment6 - treatment10 -55.00 23.93 6 -2.299 0.061
#> treatment6 - treatment11 83.25 26.75 6 3.112 0.021 *
#> treatment6 - treatment12 94.25 26.75 6 3.523 0.012 *
#> treatment7 - treatment8 132.75 26.75 6 4.962 0.003 **
#> treatment7 - treatment9 22.50 26.75 6 0.841 0.433
#> treatment7 - treatment10 -91.25 26.75 6 -3.411 0.014 *
#> treatment7 - treatment11 47.00 23.93 6 1.964 0.097
#> treatment7 - treatment12 58.00 23.93 6 2.424 0.052
#> treatment8 - treatment9 -110.25 26.75 6 -4.121 0.006 **
#> treatment8 - treatment10 -224.00 23.93 6 -9.362 0.000 ***
#> treatment8 - treatment11 -85.75 26.75 6 -3.205 0.018 *
#> treatment8 - treatment12 -74.75 26.75 6 -2.794 0.031 *
#> treatment9 - treatment10 -113.75 26.75 6 -4.252 0.005 **
#> treatment9 - treatment11 24.50 26.75 6 0.916 0.395
#> treatment9 - treatment12 35.50 26.75 6 1.327 0.233
#> treatment10 - treatment11 138.25 26.75 6 5.168 0.002 **
#> treatment10 - treatment12 149.25 26.75 6 5.579 0.001 **
#> treatment11 - treatment12 11.00 23.93 6 0.460 0.662
#>
#> Treatment Groups
#> ================
#>
#> Method : lsd
#>
#> Treatment Adjusted Means SE df lower.CL upper.CL Group
#> 8 213.67 18.27 6 168.95 258.38 12
#> 2 228.00 9.77 6 204.10 251.90 1
#> 3 247.67 9.77 6 223.76 271.57 123
#> 1 256.00 9.77 6 232.10 279.90 1234
#> 4 264.00 9.77 6 240.10 287.90 234
#> 12 288.42 18.27 6 243.70 333.13 345
#> 5 293.92 18.27 6 249.20 338.63 345
#> 11 299.42 18.27 6 254.70 344.13 45
#> 9 323.92 18.27 6 279.20 368.63 56
#> 7 346.42 18.27 6 301.70 391.13 56
#> 6 382.67 18.27 6 337.95 427.38 67
#> 10 437.67 18.27 6 392.95 482.38 7
# Genetic variability analysis
gva.augmentedRCBD(out1)
#> Warning: P-value for "Treatment: Test" is > 0.05. Genetic variability analysis may not be appropriate for this trait.
#> $Mean
#> [1] 81.0625
#>
#> $PV
#> [1] 72.26786
#>
#> $GV
#> [1] 45.29563
#>
#> $EV
#> [1] 26.97222
#>
#> $GCV
#> [1] 8.302487
#>
#> $`GCV category`
#> [1] "Low"
#>
#> $PCV
#> [1] 10.48703
#>
#> $`PCV category`
#> [1] "Medium"
#>
#> $ECV
#> [1] 6.406759
#>
#> $hBS
#> [1] 62.67743
#>
#> $`hBS category`
#> [1] "High"
#>
#> $GA
#> [1] 10.99216
#>
#> $GAM
#> [1] 13.5601
#>
#> $`GAM category`
#> [1] "Medium"
#>
gva.augmentedRCBD(out2)
#> $Mean
#> [1] 298.4792
#>
#> $PV
#> [1] 4980.411
#>
#> $GV
#> [1] 4694.161
#>
#> $EV
#> [1] 286.25
#>
#> $GCV
#> [1] 22.95435
#>
#> $`GCV category`
#> [1] "High"
#>
#> $PCV
#> [1] 23.64387
#>
#> $`PCV category`
#> [1] "High"
#>
#> $ECV
#> [1] 5.668377
#>
#> $hBS
#> [1] 94.25248
#>
#> $`hBS category`
#> [1] "High"
#>
#> $GA
#> [1] 137.2223
#>
#> $GAM
#> [1] 45.97382
#>
#> $`GAM category`
#> [1] "High"
#>